When is it time to switch to deep neural networks from simple networks in text classification problems?
Source: https://blog.easysol.net/building-ai-applications/

When data is too big, complex and nonlinear it's time to try deep learning. It's always good to try to add some layers to see it can eliminate bias and don't lead to high variance. 

Deep learning models can be tweaked(hyperparameters) and regularized(parameters), and it is worth the work.